A new noise robust ensemble method called "Averaged Boosting (A-Boosting)" is proposed. Using the hypothetical ensemble algorithm in Hilbert space, we explain that A-Boosting can be understood as a method of constructing a sequence of hypotheses and coefficients such that the average of the product of the base hypotheses and coefficients converges to the desirable function. Empirical studies showed that A-Boosting outperforms Bagging for low noise cases and is more robust than AdaBoost to label noise.